Binance founder and chief executive Changpeng Zhao, told BBC Radio 4's Today programme: "Many normal Russians do not agree with war."
Major cryptocurrency exchanges have been asked by Ukraine to block Russian users.
One financial expert warned the war could become a "crypto conflict".
In a tweet sent on Sunday Ukraine's Deputy Prime Minster Mykhailo Fedorov asked major crypto-currency exchanges to block the addresses of ordinary Russian users, not just politicians.
The value of Bitcoin has risen 13% since the Russian invasion of Ukraine, according to the Reuters news agency.
There has been speculation Russian oligarchs may pour their money into cryptocurrencies to avoid sanctions and other restrictions.
And the Telegraph newspaper called cryptocurrency "Putin's sanctions-busting super-weapon".
But Mr Zhao said: "We're not against any people.
"We differentiate between the Russian politicians who start wars and the normal people.
"Many normal Russians do not agree with war."
"We don't control the industry.
"I can publish my sanction list, you can publish yours.
"Guess what? No-one else is going to follow.
"It just moves Russian users to other smaller platforms."
In a statement published earlier, Binance said it would not unilaterally freeze millions of "innocent users'" accounts.
"Crypto is meant to provide greater financial freedom for people across the globe," the company told BBC News.
Any unilateral ban would "fly in the face" of the reason crypto existed.
But "while minimising the impact to innocent users", it was taking the steps necessary to enforce sanctions.
Mr Zhao said: "There are, I think, a few hundred individuals that are on the international sanction list in Russia - those are mostly politicians, et cetera.
"We follow that very, very strictly.
"And we are not in a position to sanction populations of people.
"We are not political - we are against war but we are here to help the people."
Several other cryptocurrency exchanges have also ruled out freezing all Russian accounts, according to a Vice News investigation.
Kraken's chief executive Jesse Powell, for example, said its platform would not freeze Russian accounts, which would go against Bitcoin's "libertarian values".
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